What conditions cause food coloring to form a compound on the surface of egg?

Food coloring doesn't form a compound on the surface of an egg in the typical sense of a chemical reaction. Here's why:

* Surface Tension: The primary reason you see food coloring congregating on the surface of an egg is due to surface tension. The egg white has a higher surface tension than water, meaning the molecules at the surface are more attracted to each other than to the air. This creates a "skin" that resists penetration.

* Dye Properties: Food coloring is typically a water-soluble dye. When you add it to water, it disperses and dissolves. However, the egg white is mostly protein, and proteins are less likely to dissolve in water. So, the dye stays primarily in the water and doesn't easily penetrate the egg white.

* Diffusion: Over time, some dye will diffuse into the egg white, but this is a slow process. The denser protein matrix of the egg white hinders the rapid movement of dye molecules.

So, it's not a chemical reaction forming a compound, but rather a combination of surface tension, dye properties, and diffusion that results in the food coloring staying on the surface.

Important Note: If you're using very strong concentrations of food coloring or certain types of dyes, there might be some minor chemical interactions with the egg proteins. But in general, the effect of food coloring on an egg is mostly a physical phenomenon.